Boundary Crossing Random Walks, Clinical Trials, and Multinomial Sequential Estimation

Sequential Analysis

Volumn 31, Issue 1, 2012, Pages 99-107

  Bibbona, Enrico ^a   Rubba, Alessandro ^a  

^a UNIVERSITY OF TURIN   (Italy)

Author keywords

Absorbed random walks; Clinical trials; Killed random walks; Sequential multinomial estimation; Unbiased estimates

Indexed keywords

EID: 84858235735     PISSN: 07474946     EISSN: 15324176     Source Type: Journal    
DOI: 10.1080/07474946.2012.652014     Document Type: Article

References (20)

1. Bhat, B. R. and Kulkarni, N. V. (1966). On Efficient Multinomial Estimation, Journal of Royal Statistical Society, Series B 28: 45-52.
2. Bibbona, E. and Ditlevsen, S. (2012). Estimation in Discretely Observed Diffusions Killed at a Threshold, arXiv 1011.1356v2.
3. Booth, C. M., Calvert, A. H., Giaccone, G., Lobbezoo, M. W., Eisenhauer, E. A., and Seymour, L. K. (2008). Design and Conduct of Phase II Studies of Targeted Anticancer Therapy: Recommendations from the Task Force on Methodology for the Development of Innovative Cancer Therapies (MDICT), European Journal of Cancer 44: 25-29.
4. Dent, S., Zee, B., Dancey, J., Hanauske, A., Wanders, J., and Eisenhauer, E. (2001). Application of a New Multinomial Phase II Stopping Rule Using Response and Early Progression, Journal of Clinical Oncology 19: 785-791.
5. Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2, second edition, New York: Wiley.
6. Ferguson, T. S. (1967). Mathematical Statistics: A Decision Theoretic Approach, New York: Academic Press.
7. Freidlin, B., Dancey, J., Korn, E. L., Zee, B., and Eisenhauer, E. (2002). Multinomial Phase II Trial Designs, Journal of Clinical Oncology20: 599.
8. Girshick, M. A., Mosteller, F., and Savage, L. J. (1946). Unbiased Estimates for Certain Binomial Sampling Problems with Applications, Annals of Mathematical Statistics 17: 13-23.
9. Goffin, J. R., Pond, G. R., and Tu, D. (2011). A Comparison of a New Multinomial Stopping Rule with Stopping Rules of Fleming and Gehan in Single Arm Phase II Cancer Clinical Trials, BMC Medical Research Journal 11: 95.
10. Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials, London: Chapman & Hall.
11. Jung, S. and Kim, K. (2004). On the Estimation of the Binomial Probability in Multistage Clinical Trials, Statistics in Medicine 23: 881-896.
12. Kocherginsky, M., Cohen, E. E. W., and Karrison, T. (2009). Design of Phase II Cancer Trials for Evaluation of Cytostatic/Cytotoxic Agents, Journal of Biopharmaceutical Statistics 19: 524-529.
13. Koike, K.-I. (1993). Unbiased Estimation for Sequential Multinomial Sampling Plans, Sequential Analysis 12: 253-259.
14. Kremers, W. K. (1990). Completeness and Unbiased Estimation in Sequential Multinomial Sampling, Sequential Analysis 9: 43-58.
15. Savage, L. J. (1947). A Uniqueness Theorem for Unbiased Sequential Binomial Estimation, Annals of Mathematical Statistics 18: 295-297.
16. Sinha, B. K., Das, K. K., and Mukhoti, S. K. (2008). On Some Aspects of Unbiased Estimation of Parameters in Quasi-Binomial Distributions, Communications in Statistics-Theory and Methods 37: 3023-3028.
17. Sinha, B. K. and Sinha, B. K. (1992). Unbiased Sequential Binomial Estimation, Current Issues in Statistical Inference: Essays in Honor of D. Basu, IMS Lecture Notes 17: 75-85.
18. Whitehead, J. (1986). On the Bias of Maximum Likelihood Estimation Following a Sequential Test, Biometrika 73: 573-581.
19. Zee, B., Melnychuk, D., Dancey, J., and Eisenhauer, E. (1999). Multinomial Phase II Cancer Trials Incorporating Response and Early Progression, Journal of Biopharmaceutical Statistics 9: 351-363.
20. Recommended by N. Mukhopadhyay